Probability

Let C1 and C2 be two biased coins such that the probabilities of getting head in a single toss are

2

3

and

1

3

, respectively. Suppose α is the number of heads that appear when C1 is tossed twice, independently, and suppose β is the number of heads that appear when C2 is tossed twice, independently. Then the probability that the roots of the quadratic polynomial x2−αx+β are real and equal, is